The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

Abstract

This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm.

Least square algorithm based on bias compensated principle for parameter estimation of canonical state space model

“…13 Wang et al proposed a parameter and state estimation algorithm based on bias compensation for observable canonical state space systems with colored noise, which can generate unbiased parameter estimation by the bias correction term. 14 For Hammerstein autoregressive moving average (ARMAX) systems with autoregressive variables, Zhang et al proposed an RLS identification method based on the BCP. 15 Wu et al combined bias compensation technology with LS estimation algorithm with forgetting factor to estimate parameters of output error model with moving average noise, 16 then, proposed an LS algorithm based on BCP for parameter estimation of MISO system under white noise.…”